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duvergers law is not a mathematical proof. it isn't even a law. it's a tautology.
I’m not going to waste my time by spelling out full academic mathematical proofs for a concept that is fucking obvious if you look at the info provided.
You obviously have no interest/capability of holding a good faith conversation
your accusation of bad faith is, itself, bad faith
duverger's law is a tautology because, from a critical rationalist perspective, a tautological statement cannot be empirically tested or falsified. it's true by definition. duverger's law states that a plurality-rule election system tends to favor a two-party system. however, if this law is framed in such a way that any outcome can be rationalized within its parameters, then it becomes unfalsifiable. for example, if a country with a plurality-rule system has more than two parties, one might argue that the system still "tends to" favor two parties, and the current state is an exception or transition phase. this kind of reasoning makes the law immune to counterexamples, and thus, it operates more as a tautological statement than an empirical hypothesis. the critical rationalist critique of marginalist economics, which relies on ceteris paribus (all else being equal) conditions, suggests any similarly structured law should be viewed with skepticism. for duverger's law to be more than a tautology, it would need to be stated in a way that allows for clear empirical testing and potential falsification, without the possibility of explaining away any contradictory evidence. this would make it a substantive theory that can contribute to our understanding of political systems rather than a mere tautology.